Introduction to logic

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Introduction to logic / by Patrick Suppes

資料種別:: 図書
出版情報:: Princeton, N.J. : D. Van Nostrand, c1957
形態:: xviii, 312 p. ; 24 cm
シリーズ名:: The university series in undergraduate mathematics <BA03828629>
著者名:: Suppes, Patrick, 1922- <DA00031944>
ISBN:: 9780442080723 [0442080727] (: hard)
書誌ID:: BA06786208

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注記:

Includes index

主題:

Logic

言語:

英語

目次情報:

Preface

Introduction

Principles of Inference and Definition / Part I：

The Sentential Connectives / Chapter 1.：

Negation and Conjunction / 1.1：

Disjunction / 1.2：

Implication: Conditional Sentences / 1.3：

Equivalence: Biconditional Sentences / 1.4：

Grouping and Parentheses / 1.5：

Truth Tables and Tautologies / 1.6：

Tautological Implication and Equivalence / 1.7：

Sentential Theory of Inference / Chapter 2.：

Two Major Criteria of Inference and Sentential Interpretations / 2.1：

The Three Sentential Rules of Derivation / 2.2：

Some Useful Tautological Implications / 2.3：

Consistency of Premises and Indirect Proofs / 2.4：

Symbolizing Everyday Language / Chapter 3.：

Grammar and Logic / 3.1：

Terms / 3.2：

Predicates / 3.3：

Quantifiers / 3.4：

Bound and Free Variables / 3.5：

A Final Example / 3.6：

General Theory of Inference / Chapter 4.：

Inference Involving Only Universal Quantifiers / 4.1：

Interpretations and Validity / 4.2：

Restricted Inferences with Existential Quantifiers / 4.3：

Interchange of Quantifiers / 4.4：

General Inferences / 4.5：

Summary of Rules of Inference / 4.6：

Further Rules of Inference / Chapter 5.：

Logic of Identity / 5.1：

Theorems of Logic / 5.2：

Derived Rules of Inference / 5.3：

Postscript on Use and Mention / Chapter 6.：

Names and Things Named / 6.1：

Problems of Sentential Variables / 6.2：

Juxtaposition of Names / 6.3：

Transition From Formal to Informal Proofs / Chapter 7.：

General Considerations / 7.1：

Basic Number Axioms / 7.2：

Comparative Examples of Formal Derivations and Informal Proofs / 7.3：

Examples of Fallacious Informal Proofs / 7.4：

Further Examples of Informal Proofs / 7.5：

Theory of Definition / Chapter 8.：

Traditional Ideas / 8.1：

Criteria for Proper Definitions / 8.2：

Rules for Proper Definitions / 8.3：

Definitions Which are Identities / 8.4：

The Problem of Division by Zero / 8.5：

Conditional Definitions / 8.6：

Five Approaches to Division by Zero / 8.7：

Padoa's Principle and Independence of Primitive Symbols / 8.8：

Elementary Intuitive Set Theory / Part II：

Sets / Chapter 9.：

Membership / 9.1：

Inclusion / 9.3：

The Empty Set / 9.4：

Operations on Sets / 9.5：

Domains of Individuals / 9.6：

Translating Everyday Language / 9.7：

Venn Diagrams / 9.8：

Elementary Principles About Operations on Sets / 9.9：

Relations / Chapter 10.：

Ordered Couples / 10.1：

Definition of Relations / 10.2：

Properties of Binary Relations / 10.3：

Equivalence Relations / 10.4：

Ordering Relations / 10.5：

Operations on Relations / 10.6：

Functions / Chapter 11.：

Definition / 11.1：

Operations on Functions / 11.2：

Church's Lambda Notation / 11.3：

Set-Theoretical Foundations of the Axiomatic Method / Chapter 12.：

Set-Theoretical Predicates and Axiomatizations of Theories / 12.1：

Isomorphism of Models for a Theory / 12.3：

Example: Probability / 12.4：

Example: Mechanics / 12.5：

Index

Preface

Introduction

Principles of Inference and Definition / Part I：

The Sentential Connectives / Chapter 1.：

Negation and Conjunction / 1.1：

Disjunction / 1.2：

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